How to change armature animation so it depends on rotation not translation
You can create new bones within the head, add a stretch to constraint and then bake the animation to get bones that rotate and scale and not translate.


Select a bone on the face (forehead1 in this example)
Snap cursor to bone ShiftS Cursor to Selected
Select tip of the base bone (that is parent of all others)
Extrude a new bone E
Snap the tip of the new bone to the target bone ShiftS Selected to cursor
Name the new bone to forehead1.new (see later)
Add a stretch to constraint and set the target to Armature then bone to forehead1


Repeat these steps for each bone

Bake the animation (Pose->Animation->Bake action, enable visual keying and clear constraints), this will turn the movement created by the constraints into rotations and scales for the bone so that the constraint can be removed. This allows the final animation data to be exported as constraints are blender specific.


select forehead1 and delete the bone
select forehead1.new and rename it to forehead1


Repeat for each bone

This is needed to keep the vertex weights in effect for the new bones, giving the new bones control of deforming the mesh. If you rename the original bone the vertex group will get renamed to match, therefore we need to delete the original bone and rename the new bone to match after the animation has been baked.

Edit:
I have made an addon called Rotation Armature to perform this task. Save the script from the link, then install and enable it you will then find a button in the tools tab called Create rotational bones which will perform the steps listed above. This is currently rather specific to the test armature you used, I may update it later to be more versatile.